Edit 2:

Now for a more serious attempt at something efficient..

findPoints =
  Compile[{{n, _Integer}, {low, _Real}, {high, _Real}, {minD, _Real}},
   Block[{data = RandomReal[{low, high}, {1, 2}], k = 1, rv, temp},
    While[k < n,
     rv = RandomReal[{low, high}, 2];
     temp = Transpose[Transpose[data] - rv];
     If[Min[Sqrt[(#.#)] & /@ temp] > minD,
      data = Join[data, {rv}];
      k++;
      ];
     ];
    data
    ]
   ];

And to test it for benchmarking...

npts = 350;
minD = 3;
low = 0;
high = 100;

AbsoluteTiming[pts = findPoints[npts, low, high, minD];]

==> {0.0312004, Null}

Check that the min distance is less than the threshold.

Min[
  MapThread[
   EuclideanDistance, {pts, Nearest[pts][#, 2][[-1]] & /@ pts}]] > minD

==> True

Check that I generated the correct number of points..

Length[pts] == npts

==> True

This is not an efficient answer but it is fun to play with so I thought I'd post it. For efficiency the use of Nearest might provide a good starting point.

g[n_, {low_, high_}, minDist_, step_: 1] := 
 Block[{data = RandomReal[{low, high}, {n, 2}], temp, happy, sdata, 
   hdata},
  
  While[True,
   temp = ((Nearest[data][#, 2][[-1]] & /@ data));
   happy = 
    Boole@Thread[MapThread[EuclideanDistance, {temp, data}] > minDist];
   hdata = Pick[data, happy, 1];
   sdata = Pick[data, happy, 0];
   If[sdata === {}, Break[]];
   sdata += RandomReal[{-step, step}, {Length[sdata], 2}];
   data = Join[sdata, hdata];
   ];
  data
  ]

The idea is to do an initial sampling and then allow the points that are too close to "walk" somewhere else. The function takes a desired number of points n, a low and high value for the data range, the minimum acceptable distance between points minDist and a step argument which allows points to "walk" up to a certain distance in the x and y directions.

Its especially fun to watch dynamically.

g[150, {0, 30}, 1.5, 1]

This is not an efficient answer but it is fun to play with so I thought I'd post it. For efficiency the use of Nearest might provide a good starting point.

g[n_, {low_, high_}, minDist_, step_: 1] := 
 Block[{data = RandomReal[{low, high}, {n, 2}], temp, happy, sdata, 
   hdata},
  
  While[True,
   temp = ((Nearest[data][#, 2][[-1]] & /@ data));
   happy = 
    Boole@Thread[MapThread[EuclideanDistance, {temp, data}] > minDist];
   hdata = Pick[data, happy, 1];
   sdata = Pick[data, happy, 0];
   If[sdata === {}, Break[]];
   sdata += RandomReal[{-step, step}, {Length[sdata], 2}];
   data = Join[sdata, hdata];
   ];
  data
  ]

The idea is to do an initial sampling and then allow the points that are too close to "walk" somewhere else. The function takes a desired number of points n, a low and high value for the data range, the minimum acceptable distance between points minDist and a step argument which allows points to "walk" up to a certain distance in the x and y directions.

Its especially fun to watch dynamically.

g[150, {0, 30}, 1.5, 1]

Edit: Per suggestion of Yves Klett the points are colored by relative happiness (green being more happy, red being less happy).